## Abstract

For a graph G, a partiteness k ≥ 2 and a number of colours c, we define the multipartite Ramsey number r^{c}_{k}(G) as the minimum value m such that, given any colouring using c colours of the edges of the complete balanced k-partite graph with m vertices in each partite set, there must exist a monochromatic copy of G. We show that the question of the existence of r^{c}_{k}(G) is tied up with what monochromatic subgraphs are forced in a c-colouring of the complete graph K_{k}. We then calculate the values for some small G including r^{2}_{3} (C_{4}) = 3, r^{2}_{4}(C_{4}) = 2, r^{3}_{3}(C_{4}) = 7 and r^{2}_{3}(C_{6}) = 3.

Original language | English |
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Pages (from-to) | 23-31 |

Number of pages | 9 |

Journal | Ars Combinatoria |

Volume | 58 |

Publication status | Published - Jan 2001 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics